# GATE Questions & Answers of Networks Electronics and Communication Engg

#### Networks 106 Question(s) | Weightage 11 (Marks)

The $ABCD$ matrix for a two-port network is defined by:

$\begin{bmatrix}V_1\\I_1\end{bmatrix}=\begin{bmatrix}A&B\\C&D\end{bmatrix}\begin{bmatrix}V_2\\-I_2\end{bmatrix}$ The parameter $B$ for the given two-port network (in ohms, correct to two decimal places) is _______.

For the circuit given in the figure, the voltage $V_C$ (in volts) across the capacitor is For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 second after closing the switch is _______. Consider the network shown below with $R_1=1\Omega,\;R_2=2\Omega\;$ and $R_3=3\Omega$. The network is connected to a constant voltage source of 11V. The magnitude of the current (in amperes, accurate to two decimal places) through the source is _______.

In the circuit shown, the positive angular frequency ω (in radians per second) at which the magnitude of the phase difference between the voltages V1 and V2 equals $\frac{\mathrm{\pi }}{4}$ radians, is_________. The figure shows an RLC circuit excited by the sinusoidal voltage 100 cos(3t) Volts, where t is in seconds. The ratio is___________. In the circuit shown, V is a sinusoidal Voltage source. The current I is in phase with voltage V. The ratio is___________. A connection is made consisting of resistance A in series with a parallel combination of resistance B and C. Three resistors of value 10 $\Omega$, 5 $\Omega$, 2 $\Omega$ are provided. Consider all possible permutations of the given resistors into the position A, B, C and identify the configuration with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to maximum values of the resistance (up to second place) is_____________.

Consider the circuit shown in the figure. The Thevenin equivalent resistance (in $\Omega$) across P-Q is__________

Consider a two-port network with the transmission matrix: $T=\left(\begin{array}{cc}A& B\\ C& D\end{array}\right)$. If the network is reciprocal, then

An AC voltage source V = 10 sin(t) volts is applied to the following network. Assume that R1 = 3 kΩ, R2 = 6 kΩ and R3 = 9 kΩ, and that the diode is ideal. RMS current Irms (in mA) through the diode is ________

In the circuit shown in the figure, the maximum power (in watt) delivered to the resistor R is __________ In the circuit shown below,VS is a constant voltage source and IL is a constant current load. The value of IL that maximizes the power absorbed by the constant current load is

The switch has been in position 1 for a long time and abruptly changes to position 2 at t=0. If time t is in seconds, the capacitor voltage VC (in volts) for t > 0  is given by

The figure shows an RLC circuit with a sinusoidal current source. At resonance, the ratio $\left|{\mathbf{I}}_{\mathbf{L}}\right|/\left|{\mathbf{I}}_{\mathbf{R}}\right|$, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is ________

The z-parameter matrix for the two-port network shown is

where the entries are in Ω. Suppose Then the value of Rb (in Ω) equals ________

In the given circuit, each resistor has a value equal to 1 Ω. What is the equivalent resistance across the terminals a and b ?

In the circuit shown in the figure, the magnitude of the current (in amperes) through R2 is ___ In the RLC circuit shown in the figure, the input voltage is given by

$v_i\left(t\right)=2\;\cos\left(200t\right)+4\;\sin\left(500t\right)$

The output voltage $v_0\left(t\right)$ is Assume that the circuit in the figure has reached the steady state before time t=0 when the 3 Ω resistor suddenly burns out, resulting in an open circuit. The current i(t) (in ampere) at t=0+ is __________ In the figure shown, the current i (in ampere) is __________ The z-parameter matrix $\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\end{bmatrix}$ for the two-port network shown is In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ______ . In the network shown in the figure, all resistors are identical with R = 300 $\mathrm{\Omega }$. The resistance Rab (in $\mathrm{\Omega }$) of the network is __________. In the given circuit, the values of $V_1$ and $V_2$ respectively are The damping ratio of a series $RLC$ circuit can be expressed as

In the given circuit, the maximum power (in Watts) that can be transferred to the load RL is ____. The voltage (VC) across the capacitor (in Volts) in the network shown is _______ In the circuit shown, the average value of the voltage Vab (in Volts) in steady state condition is _______. The 2-port admittance matrix of the circuit shown is given by An LC tank circuit consists of an ideal capacitor C connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is

In the circuit shown, the Norton equivalent resistance (in Ω) across terminals a-b is ___________. For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b is _____. In the circuit shown, the voltage Vx (in Volts) is ____. At very high frequencies, the peak output voltage Vo (in Volts) is_____. In the circuit shown, the current I flowing through the 50 Ω resistor will be zero if the value of capacitor C (in μF) is _______. The ABCD parameters of the following 2-port network are For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z1 of the first section to the input impedance Z2 of the second section is

Consider the configuration shown in the figure which is a portion of a larger electrical network For R=1 Ω and currents i1=2 A,i4=−1 A,i5= −4 A, which one of the following is TRUE?

A Y-network has resistances of 10Ω each in two of its arms, while the third arm has a resistance of 11 Ω. In the equivalent Δ-network, the lowest value (in Ω.) among the three resistances is ________

A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power factor and the second one draws 10 kVA at 0.8 lagging power factor. The complex power delivered by the source is

A periodic variable x is shown in the figure as a function of time. The root-mean-square (rms) value of x is _________. In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is________. Norton’s theorem states that a complex network connected to a load can be replaced with an equivalent impedance

In the figure shown, the ideal switch has been open for a long time. If it is closed at t=0, then the magnitude of the current (in mA) through the 4 kΩ resistor at t= 0+ is _______. In the h-parameter model of the 2-port network given in the figure shown, the value of h22 (in S) is ______ . In the figure shown, the capacitor is initially uncharged. Which one of the following expressions describes the current I(t) (in mA) for t >0? A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage VS, the resistance R, the capacitance C, and the current i(t) is given below:

${V}_{s}=Ri\left(t\right)+\frac{1}{C}{\int }_{0}^{t}i\left(u\right).$

Which one of the following represents the current i(t)?

In the figure shown, the value of the current I (in Amperes) is __________. Consider the building block called ‘Network N’ shown in the figure.
Let C = 100 μF and R = 10 kΩ. Two such blocks are connected in cascade, as shown in the figure. The transfer function $\frac{{V}_{3}\left(s\right)}{{V}_{1}\left(s\right)}$ of the cascaded network is

In the circuit shown in the figure, the value of node voltage V2 is In the circuit shown in the figure, the angular frequency ω (in rad/s), at which the Norton equivalent impedance as seen from terminals b-b′ is purely resistive, is _________. For the Y-network shown in the figure, the value of R1 (in Ω) in the equivalent Δ-network is ____. The circuit shown in the figure represents a The steady state output of the circuit shown in the figure is given by

$y\left(t\right)=A\left(\omega\right)\sin\left(\omega t+\phi\left(\omega\right)\right).$If the amplitude $\left|A\left(\omega \right)\right|=0.25$ , then the frequency $\omega$ is In the circuit shown in the figure, the value of v0(t) (in Volts) for t→∞ is ______. For the two-port network shown in the figure, the impedance (Z) matrix (in Ω) is Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding star equivalent will be scaled by a factor of The transfer function $\frac{{V}_{2}\left(s\right)}{{V}_{1}\left(s\right)}$ of the circuit shown below is A source ${v}_{s}\left(t\right)=Vcos100\pi t$ has an internal impedance of $\left(4+j3\right)\Omega$ . If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\Omega$  should be

In the circuit shown below, if the source voltage VS = $100\angle 53.13°$ V then the Thevenin’s equivalent voltage in Volts as seen by the load resistance RL is The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage VWX1 = 100V is applied across WX to get an open circuit voltage VYZ1  across YZ. Next, an ac voltage VYZ2 =100V is applied across YZ to get an open circuit voltage VWX2 across WX. Then, VYZ1 / VWX1, VWX2 / VYZ2 are respectively, Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, their effective Q factor at the same operating frequency is

Three capacitors C1, C2 and C3 whose values are 10μF, 5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe voltage in Volts that can be applied across the combination, and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively, Consider the following figure The current IS in Amps in the voltage source, and voltage VS in Volts across the current source respectively, are

Consider the following figure The current in the 1 $\Omega$ resistor in Amps is

In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is The average power delivered to an impedance (4-j3)$\Omega$ by a current $5\mathrm{cos}\left(100\pi t+100\right)A$ is

The impedance looking into nodes 1 and 2 in the given circuit is In the circuit shown below, the current through the inductor is Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is If VA-VB=6V, then VC-VD is With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

(i) 1Ω connected at port B draws a current of 3 A
(ii) 2.5Ω connected at port B draws a current of 2 A With 10 V dc connected at port A, the current drawn by 7Ω connected at port B is

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

(i) 1Ω connected at port B draws a current of 3 A
(ii) 2.5Ω connected at port B draws a current of 2 A For the same network, with 6 V dc connected at port A, 1Ω connected at port B draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is

In the circuit shown below, the Norton equivalent current in amperes with respect to the terminals P and Q is In the circuit shown below, the value of RL such that the power transferred to RL is maximum is The circuit shown below is driven by a sinusoidal input vi = Vp cos (t /RC). The steady state output vo is In the circuit shown below, the network N is described by the following Y matrix:

$Y=\left[\begin{array}{cc}0.1\mathrm{S}& -0.01\mathrm{S}\\ 0.01\mathrm{S}& 0.1\mathrm{S}\end{array}\right]$. The voltage gain $\frac{{V}_{2}}{{V}_{1}}$ is In the circuit shown below, the initial charge on the capacitor is 2.5 mC, with the voltage polarity as indicated. The switch is closed at time t=0. The current i(t) at a time t after the switch is closed is In the circuit shown below, the current I is equal to For the two-port network shown below, the short-circuit admittance parameter matrix is For parallel RLC circuit, which one of the following statements is NOT correct?

If the scattering matrix [S] of a two port network is

$\left[\mathrm{s}\right]=\left[\begin{array}{cc}0.2\angle {0}^{o}& 0.9\angle {90}^{o}\\ 0.9\angle {90}^{o}& 0.1\angle {90}^{o}\end{array}\right]$

then the network is  